Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers

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We give a short proof for a formula for the number of divisions of a convex (sn+2)-gon along non-crossing diagonals into (sj+2)-gons, where 1<=j<=n-1. In other words, we consider dissections of an (sn+2)-gon into pieces which can be further subdivided into (s+2)-gons. This formula generalizes the formulas for classical numbers of polygon dissections: Euler-Catalan number, Fuss number and Kirkman-Cayley number. Our proof is elementary and does not use the method of generating functions.
9 pages, 4 figures

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Combinatorics, 05A

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http://salesiana.dossiersoluciones.com/handle/123456789/77710

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9811086
 http://arxiv.org/abs/math/9811086

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arXiv